A Day in the Life Of...

As a technology based school, we are often required to keep up or ahead of the ITC curve. What follows is a brief overview of what you might see if you enter a Lockerby Composite School math classroom.

At the beginning of class, teachers will review an entry card from the previous day. Often, we use the iPevo document camera/app to look at common mistakes. Here is an example of “My Favorite No.”

When we finish this, we look at the new entry card. Depending on how onerous the previous day’s lesson is, our entry card is either done in a Hilroy notebook, or we use the Socrative App as a quick skills check in.
The nice thing about Socrative is the immediate feedback – we know if we can continue on to a new lesson, or if extra review is necessary.

From there, I like to use the Estimation 180 webpage as a hook. Estimation 180 is often not related to the curriculum, however it allows students an opportunity to practice their estimation skills. Over a three day period, there are three photos, each of which asks students to provide an estimate that is clearly too low, clearly too high, an estimated guess, and reasoning. Below is an example.

When possible, if there is an example of Three Acts Math that is related to the day’s expectation, we like to try to incorporate it in to the start of the lesson. Students will use whatever device they have (iPad, laptop, phone) as their media viewer to access the problem. As an example, when I taught the idea of proportions to my Grade 9 Applied class, we used the Three Act Problem – Dueling Discounts, seen below.

From this image, students were presented with a number of products, and had to determine which coupon would be the best option. Act Three is typically an extension question, and for this particular problem, it was about when each coupon would be more beneficial in general. (i.e. what if you were holding two coupons, one that said "$x off" and the other said "x% off)

Once students have had an opportunity to work through a Three Act problem, typically we either tie the lesson together in some way. A few examples of how we could do this:

• Students could summarize a video from Khan Academy, ClipKwik or TeacherTube (they would do this using some type of digital editor, as we are trying to go paperless)
• Students could access a PDF note using Dropbox and use neu.Annotate to modify a teacher led lesson/discussion on the topic
• Students could create a summary video of the topic using Educreations/Knowmia

From here, typically, students are given an opportunity to practice their new skills in some way – often from the textbook or from some real-life examples we have come up with or found. The students are asked to either keep copies of their work in a digital portfolio (using Evernote) or will have to use the Apple TV that is in our classrooms to mirror their work as a type of digital Bansho.

While not every lesson follows this format, or utilizes all of these components on a regular basis, I can say that our math department is incorporating all of the tools mentioned above at least in some way on a fairly regular basis.

Book Review: Video Games as a Medium for Learning, by Keith Devlin

I recently had the opportunity to read the book “Mathematics Education for a New Era: Video Games as a Medium for Learning” by Keith Devlin, and I have to say that it was an interesting read, and gave me pretty good perspective as to how video games could be used in a mathematics classroom.

First, it is important to point out that the author mentions that the games that currently exist for building math skills are simply skill builders, and not really what he would consider a game that can be used in an effective way in the classroom.

The author describes several principles that make for an ideal learning environment, of which the following were ones I felt were most useful. 

• That the learning environment be similar to a real world situation where people would use mathematics (the market, shops, etc).
• That the learning environment provides unlimited numbers of learners with the same environment.
• There should be uniform assessment means of assessing student performance.
• The environment should present the students with pre-planned learning experiences.
• The learning environment should provide for the student to explore and practice at their own pace.
• The learning environment should provide opportunity for immediate feedback.
• That there should be a ‘cost’ involved with getting something wrong, in order to motivate correction, but not make the student give up.
• The learning environment should provide an engaging experience.

These are principles that, for the most part, as teachers, we have been striving for in the classroom. In fact, the Growing Success document mentions how important the needs to self-assess, to work at an appropriate pace, and to receive feedback where necessary are. In our classrooms, we are constantly doing assessment for learning, having conversations, observing student work, providing students opportunities to assess, dialogue, and learn together.

These principles are extremely interesting to me – they are, generally, the exact same principles that make up every video game that I’ve ever played and enjoyed.

Consider an open world video game, if you will. The video game provides an immersive environment, where one can complete quests in whatever order, and at whatever speed, they would like. Most of these games provide intrinsic rewards from the beginning – we have the opportunity to ‘level up’ in some way. As well, in the video game experience, users get lots of opportunities to practice in context, which means that they are on task. Further, there is always a cost associated with playing a game – players will die, or fail their mission, or need to restart, but gamers continue to play, regardless.

Now, while no educational math games exist that meets this model, he suggests that the game environment must be “structured in such a way so that the players’ exploration moves them, overall, in the direction of learning that we, as educators, want to accomplish,” and he provides several ways for the games in question to meet these needs.

1) That the player should be able to learn by doing. The player should never be in a position where they should have to learn something prior to being able to play the game. A math game could be structured in a way so that the student can “master some key features of the interface… and use it to do things in the environment.”

2) That the game be self paced. At the beginning of most games, players are restricted in the areas in which they can reach. A beginner is ‘boxed in,’ in that they typically can’t access areas of the game that would be out of their realm, would be too difficult for them, and would discourage them. This feature is critical for mathematic learning. A slow or hesitant learner should be able to take as much time as necessary before moving on. If students are not prepared for that section of the game, something bad (a cost) happens. For example, they die within the game, but this forces them to re-evaluate and make sure they have the skills necessary to proceed in the game.

3) That there is opportunity to explore. The game should allow students to take time to explore and become familiar with new ideas and skills.

4) That the skills learned are put to immediate use. Skills learned should be “done in such a way that at that stage of the game the player can see the immediate need for that new information or skill”

5) That there are regular tests. Typically, in a video game, this comes in the form of a boss. You have to prove, within the game environment, that you have mastered skills and facts. The nice thing about these tests is that players are provided with lots of time to practice and prepare for the test. As well, since the ‘cost’ comes in the video game, failure is not public, and it is viewed as “I have not yet succeeded” rather than as a failure.

The author does mention that the tasks in the game need to be fairly real world, and provided a few situations where the math makes sense, contextually, within the game environment. He suggests the idea of obstacles (such as a locked door), where middle school mathematics could be incorporated into the idea of picking combination locks (probability, etc). There are often games in which puzzles like this exist, so it would just be a matter of making them a bit more complicated to develop mathematical thinking. Another example the author provides is the idea of an “investigation quest.” Typically, this is where a player needs to investigate an area, or search for an object, and typically happens in a stressful environment (i.e. complete this task before the monster comes back). In these instances, a player could be forced to use recall skills (times tables) under pressure. Finally, the author suggests treasure chests. In games, a player often encounters treasure chests, and the further in the game, the better the loot. He suggests that the chests “require the player to factor numbers to open them… and as they factor, they get better and better rewards.” Rather than having a teacher stand up and teach about prime factors, they have discovered the idea of factors in a real-world setting.

Often, in our classroom, we ask students to work collaboratively. Small group learning activities have become the norm. A multiplayer game would offer similar benefits. Students would be motivated by the loot that other students have earned from completing more difficult math problems; students could be encouraged to work in small groups to solve problems – providing for a deeper understanding; and students have opportunities to be ‘teachers’ for other players within the game.

While no games exist that fully meet the model above, I have had the opportunity to incorporate a video game into my classroom. The game designers of Portal 2 created several lesson plans and a Puzzle Maker that teachers could use to make their own lessons. My students had opportunities to learn about math in an interesting and engaging manner, and enjoyed the experience. Personally, I feel that it is just a matter of time before more game designers hop on the educational bandwagon, and students have experiences where they get an opportunity to play – without even realizing that learning about math is an added benefit.

All in all, I thoroughly enjoyed my read, and I’m hopeful that the games Keith Devlin describes are on the near horizon. All in all, I thoroughly enjoyed my read, and I’m hopeful that the games Keith Devlin describes are on the near horizon. 

Top Ten Tools at Lockerby Composite School

I teach at a school, in Sudbury, Ontario, that was one of the first schools in Canada to pilot a laptop education program. More recently, the program has evolved into what is now called the STEP (Science & Technology Education Program). As such, we are often trying to look at new, different technologies and tools at our school. Below are ten tools/resources that are used in the various classrooms at Lockerby Composite School, along with a little description of the tool.

1) Sony Vegas: One of the focuses of our Grade 10 students is to work on video creation. Every student in the STEP program in grade 10 is required to create a video, of their choosing. Typically, our tech department teaches the skills necessary to create and edit video. Students are free to choose their own video editing software (iMovie, Windows Movie Maker, etc), however Sony Vegas is the software that they teach for video editing. The main reason that our teachers use Sony Vegas is because it is powerful, and yet fairly straightforward to use, and more importantly, it comes with a free two week trial. Here is an example of a student created award winning video on safety.

2) XpressLab:  Students in our French Immersion classes are required to do an oral exam at the end of the semester. Our FI teacher has decided to start using XpressLab for the exam. She feels that it is powerful software, because XpressLab provides students with interactive opportunities to practice reading, listening, writing, and speaking in different languages. Further, it is an effective tool because students are able to self-assess, which allows students to build their confidence in French.

3) Desmos: It is always difficult to find good, new tools to use in the mathematics classroom. However, in our math department, we have started using the program Desmos. Desmos provides a graphing calculator to students at no cost. This allows us to replace our TI-83 graphing calculators which are really starting to show their age. The nice thing about Desmos is that it is real time. Changes occur to a graph as data is changed. As well, work from Desmos can be shared on blogs or via bit.ly. In our classrooms, we have used Desmos to explore transformations of functions, to examine distance time graphs/linear regression, and even use their knowledge of functions to create a smiley face. Below is an example

4) iPevo Cameras:  Every department in our school has been provided with iPevo cameras, and I have started replacing our math department’s cameras with iPevo Ziggi cameras. We like using the Ziggi’s for several reasons: to display student work, to take up problems, to teach about concepts in a more visual way, to let students teach/demonstrate for the class, and to archive day to day images to keep a record of curriculum. As well, the new Ziggi cameras have microphone capabilities, which is nice because teachers looking to use a flipped classroom could record their lessons with audio for sharing with students.

5)3D Printers: Recently, we purchased a 3D printer for our school. Our science and tech departments have been working on various ways that the printer could be used in the school, One example that was used in our drafting classes was to create a model for a 3D printer that would print a screwdriver. Here is an example (not one created at our school). We are also planning to use the 3D printer in science classrooms (to create cross sections of various organs), in our design classes to make prototypes of designs, and in our foods classrooms to create design models and cookie cutter templates.

6) iPad Minis: While we are technically a ‘laptop education’ school, we are trying to become more of a bring-your-own-device school. As such, our principal purchased a class set of iPad 2’s as well as a class set of iPad minis for use in the classroom. Several of our teachers have taken advantage of the iPads. As an example, our music teacher has students compose songs using GarageBand, and uses MadPad so students can experience using soundboards. As well, several of our teachers have used various presentation tools, such as EduCreations and Knomia, to have students create videos explaining concepts. Here is an example of a review video I had one of my students create on EduCreations (note: they restart several times as it is not possible to edit on EduCreations as yet).

7) NVU/Kompozer: Similarly to our Grade 10 project, our Grade 9 focus is on website creation. We have students create a website about whatever they would like, but typically we have them display student work. Typically we teach using Kompozer. We use Kompozer because it is very used friendly, which is good for even our less technical teachers and students who want to create a website that has some visual appeal – without requiring them to have any coding skill.

8) Paint.Net: Another component of our tech education classes is working on image editing. The image editing software of choice for us is paint.net, as it is free and web based. Several different photo editing concepts are taught, including cropping, background, gradient, colour correction, and creating digital collages. Students in our civics classroom used paint.net to create political satire image edits.

9) VUE: Creating a concept map or flow chart is a skill that is often seen in our classrooms. Whether brainstorming ideas, or creating an essay outline, the software of choice at our school is Vue (Visual Understanding Environment). We like VUE because it is a flexible environment for presenting and sharing digital information. VUE is effective because not only is it useful for concept mapping, but a variety of files can be imported into the environment, including CSV and RSS files. Below is an example of a concept map that can be created with VUE of the different types of polygons.

10) GPS:  We purchased a few GPS units for use in our Geography classes a few weeks ago. We use them in a variety of ways – to collect and plot data about water quality of streams flowing into some of our lakes; to examine geological features in our community, to geocache, and even to play GPS golf. The students always find these enjoyable experiences, as some of these topics can be a bit dry to learn from a textbook. 

There are many other tools and resources that are used at my school, however I felt as though this was a good variety of examples of what happens in the STEP program.

Please feel free to share any examples that you might have that would be different!

Self Directed PD: An Overview

Far too often, teachers are subject to in-services and workshops where we examine an idea or a concept that may or may not be useful for our own personal practice. A teacher may end up learning about something redundant, which they have already been incorporating successfully into their classroom, or about something which is difficult to implement into their day to day practice. Unfortunately, while many of these sessions hold value, they are typically not the most effective way for teachers to engage in professional development. Instead, we as educators can benefit from the same self-directed learning environment that we are attempting to provide our students.

There are several benefits to self directed learning when engaging in professional development.

1) Everybody can choose something they interested in: Training sometimes fails to meet the specific needs of the teacher. Every teacher has a different challenge, need, or deficiency that they have identified a need to improve. Since we are able to focus on something where we feel deficient, teachers could feel more motivated to work harder on this area of development, as they see an ‘end goal’ for themselves.

2) Everybody has their own learning style and needs: Like our students, we as teachers have a mix of different learning styles. If we are trying to provide ourselves the optimal learning opportunity, then it makes sense that we are able to direct our learning to be focused around our own specific learning style. As an example, a direct learner would try to do something with the information they are provided, where a reflective learner would prefer to think things through and understand them before acting on the information. 

3) Everybody takes ownership over their professional development: When one has ownership over their own learning, rather than simply participating in a process of knowledge transfer, they typically work harder to generate their own learning experiences. This results in learning that will make an impact on the teacher as a learner, by allowing teachers to look at what makes sense for them pedagogically.

4) Everybody has their own entry point: As an example, I look at the Technology in the Classroom 1 AQ that I completed recently. While some teachers taking this course are very ‘green’ when incorporating technology into the classroom, I feel relatively comfortable with a good number of different programs and tools. For me, I was able to extend my knowledge, because instead of being forced to learn a specific type of software, I had the freedom to look at whatever tools were interesting to me. This allows the beginning learner to look at something relatively straight forward with a slow learning curve, while the advanced learner can hop into the deep end and figure things out on their own. Personally, this holds a lot of merit, as it allows for an authentic learning experience, rather than a regurgitation of previously learned material.

Clearly, the option to self direct learning has a litany of benefits, and, when given the opportunity, I believe that teachers will take more from self-directed opportunities than from workshops and required sessions.

21st Century Tools Powerpoint